Sure, let's solve the equation [tex]\( C = \frac{5}{9} (F - 32) \)[/tex] for [tex]\( F \)[/tex] step-by-step.
### Step-by-Step Solution
1. Starting Equation:
[tex]\[
C = \frac{5}{9} (F - 32)
\][/tex]
2. Isolate [tex]\( F - 32 \)[/tex]:
To get rid of the fraction, we can multiply both sides of the equation by the reciprocal of [tex]\( \frac{5}{9} \)[/tex], which is [tex]\( \frac{9}{5} \)[/tex]. This will help us isolate [tex]\( F - 32 \)[/tex].
[tex]\[
C \cdot \frac{9}{5} = (F - 32) \cdot \frac{9}{5} \frac{5}{9}
\][/tex]
Simplifying this, we get:
[tex]\[
\frac{9}{5} C = F - 32
\][/tex]
3. Isolate [tex]\( F \)[/tex]:
Now, we need to solve for [tex]\( F \)[/tex] by getting rid of the term [tex]\( -32 \)[/tex]. We do this by adding 32 to both sides of the equation:
[tex]\[
\frac{9}{5} C + 32 = F
\][/tex]
4. Final Equation:
The resulting equation for [tex]\( F \)[/tex] in terms of [tex]\( C \)[/tex] is:
[tex]\[
F = \frac{9}{5} C + 32
\][/tex]
### Parameters
- The coefficient for [tex]\( C \)[/tex] in the equation is [tex]\( \frac{9}{5} \)[/tex], which is numerically equivalent to [tex]\( 1.8 \)[/tex].
- The constant term added to the result is [tex]\( 32 \)[/tex].
Hence, the conversion formula from degrees Celsius ([tex]\( C \)[/tex]) to degrees Fahrenheit ([tex]\( F \)[/tex]) is:
[tex]\[
F = 1.8 \cdot C + 32
\][/tex]
